- What Explains the Quantity and Quality of Local Inventive Activity?
In models of endogenous growth, knowledge, rather than tangible assets, plays a central role in the economic growth of nations. The model of Romer (1990) assumes that economic agents everywhere have free access to the stock of knowledge. Agrawal, Kapur, and McHale (2008), among many others, point out that immediate accessibility to knowledge is likely to depend on the geographic proximity of agents. This intuition has been verified in empirical studies of patterns of patent citations (Jaffe, Trajtenberg, and Henderson 1993) and in studies of knowledge spillovers among advertising agencies in New York City (Arzaghi and Henderson 2005) and, more generally, in manufacturing (Rosenthal and Strange 2001).
In earlier research, we found additional evidence of such spillovers. In particular we found that the rate of patenting per capita—or patent intensity—is about 20 percent higher in a metropolitan area with twice the employment density (jobs per square mile) of another metro area (Carlino, Chatterjee, and Hunt 2007). In addition to a number of other interesting results, we documented the importance of local research and development (R&D) inputs, in particular human capital, in explaining the inventive productivity of cities. [End Page 65]
In this paper, we extend our analysis in a number of important dimensions. First, we introduce a measure of the quality of local inventions—the number of citations a patent receives in patents obtained by subsequent inventors. These forward citations have been demonstrated to be correlated with a variety of indicators of value, and they have been used to document the highly skewed distribution in the value of patented inventions. We rely on a relatively new, and underutilized, source of citations—the Organization for Economic Cooperation and Development–European Patent Office (OECD–EPO) Patent Citations database. Using these data, we can determine whether our earlier results are sensitive to these adjustments for the quality of local inventions.
Second, we decompose our data on local academic R&D in a number of important dimensions, including the sources of R&D funding, R&D performed in different fields of science, and the mix of basic and applied R&D that is funded. This permits us to test whether the results of academic R&D are indeed homogenous. Third, we incorporate data on congressional earmarks for R&D that is largely performed by colleges and universities. We are able to compare these earmarks to the overall patterns of federal funding for academic R&D and to test for inefficiencies introduced by the allocation of funds through that process.
Adjusting for the quality of patents does not dramatically change most of the results we found using our simple measure of patents per capita. For example, regardless of whether we use an unweighted or weighted measure of patent intensity, the elasticity associated with employment density is about 0.22. In other words, doubling the employment density of a metropolitan area raises the per capita output of patents by 22 percent.
But some of our results do change. Using unweighted patents per capita, scale (that is, total employment) is not statistically significant in the regressions unless we allow for diminishing returns. With citation-weighted patents per capita, however, the implied elasticity of scale is 0.12 and statistically significant. If we do allow for diminishing returns and we adjust for the quality of inventions, we find that metro areas enjoy increasing returns to scale over a much larger range than we estimated previously. In that case, these returns are exhausted at a population of about 1.8 million. In contrast, when we do not employ citation weighting, our estimates suggest these returns to scale are exhausted for populations around 720,000.
The presence of an educated workforce is the decisive factor that explains the inventive output of cities, even after controlling for the historical mix of industries and technologies invented. Evaluated at the mean, a 10 percent increase in the share of the workforce with at least a college degree raises our [End Page 66] measures of patent intensity by about 10 percent. All else equal, a 1 standard deviation increase in our human capital variable is associated...